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    <title>LDA Overview</title>
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        <h1 align="center">LDA Overview</h1>
		<p align="left">Poisson distribution provides a method for conducting absolute quantification 
		that is independent of qPCR, which can be visually 
		demonstrated using a graph that was introduced in the 
		<a href="less_than_10molecules.html">&lt;10 Molecule 
		Problem</a> section:</p>
		<p align="center">
		<img border="0" src="images/poisson_distribution_graph.gif" width="532" height="372"></p>
		<p align="left">This indicates that the frequency of zero molecule 
		aliquots (denoted in yellow) is inversely dependent on target 
		concentration. In terms of PCR amplification, this can be expressed 
		mathematically by the equation:</p>
		<p align="center">
		<img border="0" src="images/lda_equation.gif" width="186" height="71"></p>
		<p align="left">where &quot;#nil&quot; is the number of amplification reactions 
		that fail to produce an amplification profile (i.e. 0 N aliquots), &quot;#total&quot; is the total 
		number of replicate reactions conducted and &quot;N<sub>av</sub>&quot; is the 
		target concentration. Thus, for a sample containing target quantities 
		below 1 N/<font face="Times New Roman">aliquot</font>, the target 
		concentration can be determined by conducting replicate amplification 
		reactions and counting the number of nil reactions. </p>
		<p align="left">Of greater significance, conducting absolute 
		quantification in this fashion is independent of the kinetic and optical 
		parameters upon which real-time qPCR is based, in that it relies solely 
		on the frequency of nil reactions. The only major requirements are that 
		a sufficient number of cycles be conducted to ensure amplification of 
		single target molecules, even under low amplification efficiency 
		(typically 50 cycles is sufficient), and secondly, that those reactions that produce non-specific 
		amplification products are either absent or can be identified (e.g. via 
		melting curves). </p>
		<p align="left">Referred to as &quot;limiting dilution assay&quot; or LDA, this 
		approach allows the quantitative accuracy of any qPCR assay to be assessed by 
		simply diluting the target to about 0.7 molecules per aliquot and conducting 
		16-48 replicate reactions:</p>
		<p align="center">
		<img border="0" src="images/sand_undiluted.gif" width="288" height="202"></p>
		<p align="left">In this example LRE quantification predicted a target 
		concentration of 4,504. Diluting the sample 11,000X and conducting 16 
		replicate reactions produced 10 nil reactions:</p>
		<p align="center">
		<img border="0" src="images/sand_diluted.gif" width="289" height="234"></p>
		<p align="left">LDA predicts that the concentration of the target 
		in the undiluted sample is 5,170 molecules per aliquot, which is a 
		difference of about 15% from that derived from LRE quantification.</p>
		<p align="left">See Wang, Z. and Spadoro, J. (1998) In Ferré, F. (ed.), 
		Gene Quantification. Birkhäuser, Boston, pp. 31-34 for additional 
		details about how this approach was developed, including how the number of replicate 
		reactions impacts the accuracy of the assay.</p>
		<p align="left">Note also that the third LRE overview video available on the 
		LRE qPCR website (<font color="#FF0000">sites.google.com/site/lreqpcr</font>)&nbsp; provides a detailed discussion of assessing 
		quantitative accuracy. </p>
		<p align="left">&nbsp;</p>
      	<p align="left">&nbsp;</p>
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